Wilson's Theorem in Disguise

The American Mathematical Monthly problem 10578 considers a sequence defined by recurrence equation with initial conditions and asks to show that is only an integer for prime .
This Demonstration uses Mathematica's built-in function RecurrenceTable to generate the sequence and finds for which is an integer.

SNAPSHOTS

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DETAILS

It is easy to find a symbolic solution of the above recurrence equation:
The above fraction is an integer only for prime by virtue of Wilson's theorem.
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